Answer
$x=\left\{ \dfrac{18}{11},\dfrac{1}{21} \right\}$
Work Step by Step
Equating each factor to zero (Zero Product Principle), then the solutions to the equation, $
\left( \dfrac{2}{3}x-\dfrac{12}{11} \right)\left( \dfrac{7}{4}x-\dfrac{1}{12} \right)
,$ is
\begin{array}{l}\require{cancel}
\dfrac{2}{3}x-\dfrac{12}{11}=0
\\\\
\dfrac{2}{3}x=\dfrac{12}{11}
\\\\
\dfrac{3}{2}\left(\dfrac{2}{3}x\right)=\left(\dfrac{12}{11}\right)\dfrac{3}{2}
\\\\
x=\dfrac{36}{22}
\\\\
x=\dfrac{\cancel{2}\cdot18}{\cancel{2}\cdot11}
\\\\
x=\dfrac{18}{11}
,\\\\\text{OR}\\\\
\dfrac{7}{4}x-\dfrac{1}{12}=0
\\\\
\dfrac{7}{4}x=\dfrac{1}{12}
\\\\
\dfrac{4}{7}\left(\dfrac{7}{4}x\right)=\left(\dfrac{1}{12}\right)\dfrac{4}{7}
\\\\
x=\dfrac{4}{84}
\\\\
x=\dfrac{\cancel{4}}{\cancel{4}\cdot21}
\\\\
x=\dfrac{1}{21}
.\end{array}
Hence, $
x=\left\{ \dfrac{18}{11},\dfrac{1}{21} \right\}
.$
